Slot antenna

ABSTRACT

The present invention disclosed design aspects and the measured results of a miniaturized resonant narrow slot antenna. The resonant narrow slot radiating elements have a planar geometry and are capable of transmitting vertical polarization when placed nearly horizontal. A resonant narrow slot antenna according to the present invention simplifies impedance matching. Slot dipoles can be excited by a microstrip line and can be matched to arbitrary line impedances by moving the feed point along the slot. Antenna miniaturization can be achieved by using a high permittivity or permeability substrate and superstrate materials and/or using an appropriate antenna topology. Miniaturization is achieved through providing a unique geometry for a resonant narrow slot antenna. A very efficient radiating element is provided. With the virtual enforcement of the required boundary condition at the end of a slot antenna, the area occupied by the resonant antenna can be reduced. To achieve the required virtual boundary conditions, the two short-circuit at the end of resonant slot are replaced by some reactive boundary conditions, including inductive or capacitive boundary conditions, including inductive or capacitive loadings.

FIELD OF THE INVENTION

The present invention relates to efficient miniaturized resonant slotantennas, and more particularly to loaded resonant slot antennas, orfolded resonant narrow slot antennas.

BACKGROUND OF THE INVENTION

The topic of small antennas has been of prolonged interest and goes backmore than half a century. Using the area of the substrate moreeffectively in microwave circuits, as part of a general trend inmonolithic circuit integration and antenna invisibility for certainapplications, has been among the major motivations. On the other hand,in the radio communication, where the line of sight communication is notgenerally possible, the UHF-VHF frequencies should be used. At these lowfrequencies, the size of even a single half wave dipole antenna ispreclusive in many mobile and wireless applications.

The subject of antenna miniaturization is not new. The literatureconcerning this subject date back to the early 1940's. It has been shownthat the Q factor of the equivalent circuit for each spherical mode canbe expressed in terms of the normalized radius (a/λ) of the smallestsphere enclosing the antenna and also the Q of the lowest order mode isa lower bound for the Q of a single resonant antenna. A similarprocedure is used, for characterization of a small dipole antenna usingcylindrical wave functions. Then a cylindrical enclosing surface is usedwhich produces a tighter lower bound for the Q of small antennas withlarge aspect ratios such as dipoles and helical antennas. Qualitatively,these studies show that for single resonant antennas, the smaller themaximum dimension of an antenna is, the higher the Q of the antenna orequivalently the lower the bandwidth of the antenna. However, thestudies do not provide a description of the process for practicing theminiaturization methods, antenna topology, or impedance matching.

Normally, there is a compromise between the size, efficiency andbandwidth of the antenna. It is known to address this subject byexpanding fields of an arbitrary small antenna enclosed in a sphere,using spherical eigen-functions expansion. The Q of the antenna, whichis by definition the ratio of the stored energy to the radiated power,can be related to the Q of each eigen-mode. This approach introduces alower bound on the Q of the antenna. The calculated Q is a function ofradius of the sphere or correspondingly the largest dimension of theantenna. On the other hand, a lower bound on Q in some senses is anindication of an upper limit on the antenna bandwidth. There are twoways to achieve miniaturization. One is to use a high permittivitysubstrate and the other is to exploit the substrate area in twodimensions by changing the topology of the antenna

With the advent of wireless technology and ever increasing demand forhigh data rate mobile communications the number of radios on mobileplatforms has reached a point that the available real estate for theseantennas has become a serious issue. Similar problems are also emergingin the commercial sector where the number of wireless services plannedfor future automobiles, such as FM and CD radios, analog and digitalcell phones, GPS, keyless entry and etc., is on the rise. Consideringwave propagation where line-of-sight communication is an unlikely event,such as in an urban environment or over irregular terrain, carrierfrequencies at HF-UHF band are commonly used. At these frequencies thereis considerable penetration through vegetation and buildings, wavediffraction around obstacles, and wave propagation over curved surfaces.However at these frequencies the size of efficient antennas arerelatively large and therefore a large number of such antennas may notfit in the available space without the risks of mutual coupling andco-site interference. Efficient antennas require dimensions of the orderof half a wavelength for single frequency operation. To cover a widefrequency range, broadband antennas may be used, however, dimensions ofthese antennas are comparable to or larger than the wavelength at thelowest frequency. Besides, depending on the applications, thepolarization and the direction of maximum directivity for differentwireless systems operating at different frequencies may be different andhence a single broadband antenna may not be sufficient. It should alsobe noted that any type of broadband antenna is highly susceptible toelectronic jamming techniques. Variations of monopole and dipoleantennas in use today are prohibitively large and bulky at HF throughVHP.

SUMMARY OF THE INVENTION

An important component of any wireless system is its antenna. Withrecent advances in solid state devices and MEMS technology, constructionof high performance miniaturized transmit and receive modules havebecome realizable. These modules together with miniaturized sensors andtransducers have found numerous applications in industry, medicine, andmilitary. In addition to the need for antenna miniaturization, low powercharacteristics of such transmitters and receivers are extremelyimportant as well. Whereas significant efforts have been devoted towardsachieving low power and miniaturized electronic and RF components,issues related to design and fabrication of efficient, miniaturized, andeasily integrable antennas have been overlooked. The early studies ofsmall antennas were restricted to the establishment of fundamentallimitations of these types of antennas with regard to the antenna sizeand bandwidth. In recent years, the practical aspect of antennaminiaturization has received significant attention. Most successfuldesigns, however, rely on the use of high permittivity ceramics, whichare not suitable for monolithic integration. The present inventionbuilds on the concept of a class of miniaturized, planar,re-configurable antennas, which take advantage of antenna topology forminiaturization. Using this concept, design of a miniaturized antenna assmall as 0.05λ₀×0.05λ₀ and a fairly high efficiency of −3 dBi can beaccomplished. Since there are neither polarization nor mismatch losses,the antenna efficiency is limited only by the dielectric and Ohmiclosses of the substrate on which the antenna is made. The bandwidth ofthis antenna is rather small as is the case for all miniaturizedantennas. Resonant antennas in general, and slot-dipoles in particularare inherently narrow-band. By reducing the size of a slot, the physicalaperture of the antenna is reduced and therefore, the radiationconductance of miniaturized slot antenna becomes very small. On theother hand, an infinitesimal dipole can have an effective aperture,which is as high as that of a half wavelength dipole under the impedancematched condition. One way to match the impedance of the miniaturizedslot antenna is to tune it slightly off resonance, whether capacitively,or inductively. A smaller capacitance or larger inductance is neededdepending on whether the antenna is tuned below or above the resonance.However, a smaller capacitance, or conversely a larger inductance,results in a narrower bandwidth To partially improve the bandwidth ofthe miniaturized slot antenna, the physical aperture can be increasedwithout increasing the overall size of the antenna.

The present invention takes advantage of the topology of the antenna.Generally, in resonance antennas two boundary conditions are required inconjunction with the Maxwell's equation. The natural frequency of thesystem is defined by the eigen-values of the describing equations. In asimple half wave dipole these two conditions are chosen to be an opencircuit (zero current) at both wire ends. Similarly, in the dual problemof a slot antenna, the electric field is shortened by the ground, whichgives the traditional half wavelength slot antenna. The choice of thesetwo boundary conditions is somewhat arbitrary and enforcing a morecleverly chosen boundary condition would result in a smaller antenna.The boundary condition has been devised for matching short dipoleantennas by top loading and also center loading. In what follows ageneral procedure for the design of a small slot antenna is presented.Then simulation results for prototype antennas as well as the inputimpedance and radiation patterns of the antennas are presented andcompared with the measurements. According to the present invention, thetopology of an efficient, miniaturized, resonant slot antenna isdisclosed and then the radiation, input impedance, and bandwidthcharacteristics of the antenna are investigated. This class of antennascan exhibit simultaneous band selectivity and anti-jam characteristicsin addition to possessing a planar structure and low profile, which iseasily integrable with other RE and microwave circuits.

This miniaturization for a resonant slot dipole is achieved by notingthat a slot dipole can be considered as a transmission line resonator,where at the lowest resonant frequency the magnetic current (transverseelectric field in the slot) goes to zero at each end of the dipoleantenna. At the operating frequency the antenna length l=λ_(g)/2 whereλ_(g) is the wavelength of the quasi-TEM mode supported by the slotline. In view of transmission line resonators one can also make aquarter-wave resonator by creating a short circuit at one end and anopen circuit at the other end. However, creating a physical open circuitfor slot lines is not practical. Basically, a spiral slot of a quarterwavelength and shorted at one end behaves as an open circuit at theresonant frequency. With this invention the size of the slot dipole canbe reduced by approximately 50%. Further reduction can be accomplishedby bending the radiating section. This bending procedure should be doneso that no section of the resulting line geometry carries a magneticcurrent opposing the current on any other sections.

Other applications of the present invention will become apparent tothose skilled in the art when the following description of the best modecontemplated for practicing the invention is read in conjunction withthe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The description herein makes reference to the accompanying drawingswherein like reference numerals refer to like parts throughout theseveral views, and wherein:

FIG. 1A is a magnetic current distribution on a ultra high frequency(UHF) miniaturized slot antennae illustrating the ground-plane side ofthe antennae and meshing configuration used in method of momentscalculations;

FIG. 1B is an electric current distribution on a microstrip feed of theslot antennae of FIG. 1A at the resonant frequency;

FIG. 2A is a simulated reflection co-efficient of the miniaturized UHFantennae on an infinite ground plane using Smith chart representation;

FIG. 2B is a simulated reflection co-efficient of the miniaturized UHFantennae on an infinite ground plane with magnitude of /S₁₁/ inlogarithmic scale;

FIG. 3 is a photograph of three miniaturized UHF antennas with similargeometry and dimensions while differing only in the size of the groundplane;

FIG. 4 is a graph illustrating measured magnitude of reflectionco-efficient for the three miniaturized UHF slot antennas shown in FIG.3 having the same size in geometry while having different ground planesizes;

FIG. 5A is a graph illustrating the co-polarized and cross-polarizedpattern of the miniaturized UHF antennae in H-plane;

FIG. 5B is a graph illustrating the co-polarized and cross-polarizedpattern of the miniaturized UHF antennae in E-plane;

FIG. 6 is a simulated gain of the UHF miniaturized antennae on aninfinite substrate with ε_(r)=4.0(1−j tan δ);

FIG. 7 is a simplified schematic view illustrating E-plane and H-planeof the slot antennae being tested experimentally with co-polarized andcross-polarized pattern measurements performed in the indicatedprinciple planes;

FIG. 8 is a graph illustrating magnetic current distribution of a halfwave length and inductively terminated miniaturized slot antennae;

FIG. 9A is a simplified schematic diagram of a transmission line modelof a half wave slot antennae;

FIG. 9B is a simplified schematic diagram of a transmission line modelof an inductively terminated slot antennae;

FIG. 9C is a simplified schematic diagram of a transmission line modelof a slot antennae with two series inductive terminations;

FIG. 10 is a simplified diagram illustrating an antennae geometry fed bya two-port microstrip feed to determine the exact resonant frequency ofthe inductively loaded slot;

FIG. 11 is a graph illustrating the S-parameters of the two-portantennae illustrated in FIG. 19;

FIG. 12 is a simplified schematic view illustrating the topology of anequivalent circuit for the two-port antennae;

FIG. 13 is a graph illustrating the Y-parameters of the two-portantennae after de-embedding the microstrip feed lines;

FIG. 14A through FIG. 14D illustrate comparisons between the full-wavesimulated S-parameters of the antennae and that of the equivalentcircuit;

FIG. 15 is a graph illustrating the required terminating admittance forthe second port of the two-port model in order to match the antennae toa 50Q line;

FIG. 16 is a graph illustrating measured and simulated return loss ofthe miniaturized antennae;

FIG. 17 is a simplified schematic view illustrating the geometry of aslot antennae and feed;

FIG. 18 is a photograph of a fabricated antennae according to thepresent invention;

FIG. 19 is a graph illustrating the simulated radiation pattern of theminiaturized antennae;

FIG. 20A is a graph illustrating the measured radiation pattern of theantennae with a (0.2λ_(O)×0.2λ₀) and a larger (0.5λ₀×0.5λ₀) ground planeillustrating the H-plane pattern; and

FIG. 20B is a measured radiation pattern of the antennae of FIG. 28Aillustrating the E-plane pattern

FIG. 21 is a simplified schematic view of a miniaturized folded slotantennae;

FIG. 22A is a graph illustrating impedance of a center fed miniaturizedfolded-slot antennae;

FIG. 22B is a graph illustrating impedance of a miniature slot antennaefor comparison with FIG. 12A;

FIG. 23 is a simplified schematic diagram of a capacitively fedminiaturized folded slot antennae geometry;

FIG. 24 is a graph illustrating measurement and simulation of aminiaturized folded slot antennae return loss;

FIG. 25A is a graph illustrating radiation pattern for the miniaturizedfolded slot antennae in the E-plane;

FIG. 25B is a graph illustrating the radiation pattern for theminiaturized folded slot antennae in the H-plane;

FIG. 26 is a simulated radiation pattern of the total field for theminiaturized folded slot antennae;

DESCRIPTION OF THE PREFERRED EMBODIMENT

A major reduction in size is achieved by noting that a slot dipole canbe considered as transmission line resonator where at the lowestresonant frequency the magnetic current (transverse electric field inthe slot) goes to zero at each end of the dipole antenna. As mentionedbefore at this frequency the antenna length l=λ_(g)/2 where λ_(g) is thewavelength of the quasi-TEM mode supported by the slot line. λ_(g) is afunction of substrate thickness, dielectric constant, and the slotwidth, which is shorter than the free-space wavelength In view oftransmission line resonators one can also make a quarter-wave resonatorby creating a short circuit at one end and an open circuit at the otherend. However, creating a physical open circuit for slot lines is notpractical. The present invention incorporates the idea of non-radiatingtightly coiled slot spiral. Basically, a spiral slot of a quarterwavelength and shorted at one end behaves as an open circuit at theresonant frequency. Therefore a quarter-wave slot line short-circuitedat one end and terminated by the non-radiating quarter-wave spiralshould resonate and radiate electromagnetic waves very efficiently. Withthis topology the size of the slot dipole can be reduced byapproximately 50%. Further reduction can be accomplished by bending theradiating section. This bending procedure should be done so that nosection of the resulting line geometry carries a magnetic currentopposing the current on any other sections. FIGS. 1A and 1B shows thegeometry of a typical λ_(g)/4 compact resonating slot antenna. Theradiating section is terminated with two identical quarter-wavenon-radiating spiral slots to maintain the symmetry. It was found thatby splitting the magnetic current at the end into equal and opposingmagnetic currents the radiation efficiency is enhanced. Since themagnetic current distribution attains its maximum at the end of thequarter-wave line, the magnetic current in the beginning segments of asingle (unbalanced) quarter-wave spiral reduces the radiation of theradiating section. But the opposite magnetic currents on two suchspirals simply cancel the radiated field of each other and as a resultthe radiated field of the radiating section remains intact. Someadditional size reduction can also be-achieved, by noting that thestrength of the magnetic current near the short-circuited end of theradiating section is insignificant. Hence, bending this section of theline does not significantly reduce the radiation efficiency despiteallowing opposing currents. In FIG. 1A the T-top represents a smallreduction in length of the line without affecting the radiationefficiency. This antenna is fed by an open ended microstrip line. Aquarter wavelength line corresponds to a short-circuit line under theslot, however, using the length of the microstrip line as an adjustableparameter, the reactive part of the antenna input impedance can becompensated for.

EXAMPLE I

FIGS. 1A and 1B respectively, show the electric current distribution onthe microstrip feed and the magnetic current distribution on the slot ofthe compact UHF antenna designed to operate at 600 MHZ. An ordinary FR4substrate with thickness of 3 mm (120 mil.) and dielectric constantε_(r)=4. PiCASSO™ software was used for the simulations of this antenna.The microstrip feed is constructed from two sections: 1) a 50Ω linesection, and 2) an open-ended 80Ω line. The 80Ω line is thinner whichallows for compact and localized feeding of the slot. The length of thisline is adjusted to compensate for the reactive component of the slotinput impedance. Noting that the slot appears as a series load in themicrostrip transmission line, a line length of less than λ_(m)/4compensates for an inductive reactance and a line length of longer thanλ_(m)/4 compensates for a capacitive reactance. Here λ_(m) is the guidedwavelength on the microstrip line. First a quarter wavelength sectionwas chosen for the length of the microstrip line feeding the slot. Inthis case the simulation predicts the impedance of the slot antennaalone. Through this simulation it was found that the slot antenna fednear the edge is inductive. So a length less than λ_(m)/4 is chosen forthe open-ended microstrip line to compensate for the inductive load. Thereal part of input impedance of a slot dipole depends on the feedlocation along the slot and increases from zero at the short-circuitedend to about 2000Ω at the center (quarter wavelength from the shortcircuit). This property of the slot dipole allows for matching to almostall practical transmission lines. The crossing of the microstrip lineover the slot was determined using the full-wave analysis tool,(PiCASSO™) and by trial-and-error. The uniform current distribution overthe 50Ω line section indicates no standing wave pattern, which is aresult of a very good input impedance match

Apart from the T-top section, the quarter-wave radiating section of theslot dipole is composed of three slot line sections, two vertical andone horizontal. Significant radiation emanates from the middle and lowersections. Polarization of the antenna can be chosen by changing therelative size of these two sections. In this design the relative lengthsof the three line sections were chosen in order to minimize the areaoccupied by the slot structure. The slot width of the first section canbe varied in order to obtain an impedance match as well. When there is alimitation in moving the microstrip and slot line crossing point, theslot width may be changed. At a given point from the short-circuited endan impedance match to a lower line impedance can be achieved when theslot width is narrowed. This was used in this design, as the slot linewidth of the top vertical section is narrower than the other twosections. It should be pointed out that by narrowing the slot line widththe magnetic current density increases, but the total magnetic currentin the line does not. In other words there is no discontinuity in themagnetic current along the line at points where the slot width ischanged, however, there are other consequences. One is the change in thecharacteristic impedance of the line and the second is the change in theantenna efficiency considering the finite conductivity of the groundplane. There are two components of electric current flowing on theground plane, one component flows parallel to the edge and the other isperpendicular. For narrow slots the current density of the parallelcomponent near the edge goes up and as a result this current sees ahigher ohmic resistance. The magnetic current over the T-top section isvery low and does not contribute to the radiated field but its lengthaffects the resonant frequency. Half the length of the T-top sectionoriginally was part of the first vertical section, which is removed andplaced horizontally to lower the vertical extent of the antenna.

The slot line sections were chosen so that a resonant frequency of 600MHz was achieved. At this frequency the slot antenna occupies an area of(6.5 cm×6.5 cm) or in terms of the free-space wavelength 0.12λ₀×0.12λ₀.FIGS. 2A and 2B respectively, show the simulated input impedance andreturn loss of the miniaturized UHF antenna as a function of frequency.It is shown that the 1.2 VSWR (−10 dB return loss) bandwidth of thisantenna is around 6 MHZ which corresponds to a 1% fractional bandwidth.This low bandwidth is a characteristic of miniaturized and resonant slotdipoles. The simulation also shows a weak resonance, which may be causedby the interaction between the radiating element and the non-radiatingspirals. In fact careful examination of the magnetic currentdistributions over the non-radiating spirals shows the asymmetry causedby the near field interaction of the radiating element with thenon-radiating spirals.

The polarization of this antenna may appear to be rather unpredictableat a first glance due to its convoluted geometry. However, it can beconjectured that the polarization of any miniaturized antenna whosedimensions are much smaller than a wavelength cannot be anything otherthan linear. This is basically because of the fact that the smallelectrical size of the antenna does not allow for a phase shift betweentwo orthogonal components of the radiated field required for producingan elliptical polarization. Hence by rotating the antenna a desiredlinear polarization along a given direction can be obtained.

EXAMPLE II

An antenna based on the layout shown in FIGS. 1A and 1B was made on aFR4 printed-circuit-board. In the first realization, the size of theground plane was chosen to be 8.5 cm×11 cm. The return loss of thisantenna was measured with a network analyzer and the result is shown bythe solid line in FIG. 4. It is noticed that the resonant frequency ofthis antenna is at 568 MHz, which is significantly lower than what waspredicted by the simulation. Also the measured return loss for thedesigned microstrip feed line was around −10 dB. To get a better returnloss the length of the microstrip line had to be extended slightly. FIG.4 shows the measured return loss after the modification. The gain ofthis antenna was also measured against a calibrated antenna. Under apolarization matched condition a gain of −5.0 dBi (gain in dB against anisotropic radiator) is measured. The simulated gain value of thisantenna using an infinite ground plane and ε=4.0 is found to be 2.8 dBi.The difference in the simulation results and the measured ones can beattributed to the finiteness of the ground plane, finite conductivity ofthe ground plane, and the loss-tangent of the substrate. The effect ofthe imaginary part the substrate dielectric constant (ε=4.0-jε″) can bequantified using a numerical simulation. FIG. 6 shows the simulated gainvalues of this antenna as a function of ε″ with an infinite groundplane. It is shown that, as expected, the gain is decreased when theloss tangent is increased. Hence it is very important to use substrateswith very low loss tangent. The FR4 used for this antenna has a losstangent (tan δ≈0.01) at UHF. To investigate the effect of ground planesize on the resonance frequency and radiation efficiency, two moreantennas having the same geometry and dimensions but with differentground plane sizes were made. The measured resonant frequencies are alsoshown in FIG. 4. FIG. 3 shows a photograph of these antennas. Thedimensions of the ground planes and the measured gain of these antennasare reported in Table 1. TABLE 1 The resonant frequencies gains and theground plane sizes of three identical UHF miniaturized slot antennas.Here the effect of ground plane size on the resonant frequency andantenna gain is demonstrated. Ground Plane Size Resonant Frequency Gain(dBi) Antenna 1  8.5 cm × 11 cm 568 MHZ −5.0 Antenna 2   12 cm × 13 cm577 MHz −2.0 Antenna 3 22.5 cm × 25 cm 592 MHz 0.5As expected the resonant frequency and the gain of the antennaapproaches the predicted values as the size of the ground plane isincreased. The gain of Antenna 3 is almost as high the gain of an idealdipole considering the loss-tangent of the substrate used in theseexperiments.

The gain reduction as a function of ground plane size can be explainedby noting that the equivalent magnetic currents that are flowing in theupper and lower side of the ground plane are in opposite directions. Inthe case of infinite ground plane, the upper and lower half-spaces areelectromagnetically decoupled. However, when the ground plane is finiteand small compared to the wavelength the radiated field from the lowerhalf-space can reduce the radiated field from the magnetic current inthe upper half-space. The level of back-radiation depends on the size ofthe ground plane. In other words, the smaller a ground plane is thehigher back-radiation becomes. Ignoring the substrate (ε_(r)=1),radiation from the upper and lower magnetic currents completely canceleach other in the plane of the perfect conductor (creates a null in theradiation pattern). However, because of the substrate and depending onits thickness and relative dielectric constant a perfect cancellationdoes not occur. This explains the discrepancies observed between themeasured and predicted radiation patterns (for infinite ground plane).Also there are strong edge currents on the periphery of a finite groundwhich decreases as the size of the ground plane is increased. Theconfined currents around the edge experience an ohmic loss which isresponsible for the decrease in the antenna gain.

The radiation pattern of these antennas were also measured in theUniversity of Michigan anechoic chamber. A linearly polarized antennawas used as the reference. First the polarization of the antenna wasdetermined at the direction of maximum radiation (normal to the groundplane). Then by rotating the antenna under test about the direction ofmaximum radiation, it was found that indeed the polarization of theminiaturized antenna is linear. FIG. 7 shows the direction of maximumradiation and the direction of electric field (polarization) andmagnetic field at the antenna boresight. FIGS. 5A and 5B show the co-and cross-polarized antenna patterns in the H-plane and E-plane,respectively. It is shown that the antenna polarization remains linearon these principal planes. As discussed before, the E-plane gain in theplane of the ground plane (θ=90°) drops because of the finiteness of theground plane. If the substrate were to be removed the E-plane gain inthe plane of the conductor would drop to zero. Hence having a thicksubstrate helps achieving a more uniform pattern. Thick and highpermittivity substrate also increases front-to-back radiation ratio.Since the substrate thickness is only a small fraction of thewavelength, almost similar gain values are measured in the upper andlower half-spaces.

It is worth mentioning that further miniaturization can easily beaccomplished by increasing the dielectric constant of the substrate. Inthis case the guide wavelength shortens which in turn allows for asmaller antenna. As previously mentioned further antenna miniaturizationis accompanied by a reduction of the antenna bandwidth. Also confiningthe electric currents on the ground plane into a smaller area results ina higher ohmic loss or equivalently lower antenna efficiency.

According to the present invention, a topology for an electrically smallresonant slot antenna is demonstrated. A major size reduction wasachieved by constructing a λ_(g)/4 resonant slot rather than thetraditional λ_(g)/2 antenna. This is accomplished by generating avirtual open circuit at one end of the slot. Further miniaturization wasachieved by bending the slot into three pieces in order to use the areaof the board more efficiently. The antenna geometry occupies a verysmall area (0.014 λ₀ ² of a PC board with ε_(r)=4.0 and thickness 3mm.The antenna is very efficient and shows a gain as high as a dipoleantenna and a 1% bandwidth. It is also shown that if the antenna is madeon a small ground plane its gain will be reduced and its radiationpattern changes slightly.

A novel procedure according to the present invention allows the designof a miniaturized slot antenna where its dimensions (relative towavelength) can be arbitrarily chosen depending on the applicationwithout any adverse effects on the impedance matching. As will be shown,in order to fine-tune the resonant frequency of this structure, theantenna is first fed by a two-port microstrip line, and then thelocation of the null in the insertion loss (S₂₁) is found and adjusted.To specify the terminating impedance at the second port in such a waythat a perfect match is achieved, an equivalent circuit for the antennais proposed and its parameters are extracted using a genetic algorithmin conjunction with a full-wave simulation tool. Finally, a prototypeantenna is designed, fabricated and its performance is evaluatedexperimentally.

For a resonant slot antenna, two boundary conditions (BC) are applied atboth ends of a slot line to form a resonant standing wave pattern. Thesetwo conditions are chosen to enforce zero electric current (opencircuit) for a wire antenna or zero voltage (short circuit) for the slotantenna and yield a half-wave resonant antenna. On the other hand, thesealternative BCs result in a smaller resonant length than a halfwavelength antenna. One choice which is conducive to antennaminiaturization is the combination of a short circuit and an opencircuit, which allows a shorter resonant length of λ/4. The choice ofthe two BCs, however, is not restricted to the above conditions, whereasthe effect of reactive BCs in reducing the resonant length and antennaminiaturization is investigated in what follow.

Starting from a λ_(S)/2 slot and in the view of the transmission lineapproximation for the slot dipole, the equivalent magnetic currentdistribution along a linear slot antenna can be expressed as$\begin{matrix}{{M(z)} = {M_{0}{\cos\left( {\frac{\pi}{\lambda_{s}}z} \right)}}} & (1)\end{matrix}$where λ_(g) is the guided wavelength in the slot-line. In equation (1)M₀ represents the amplitude of the magnetic current density (electricfield across the slotline). This approximate form of the currentdistribution satisfies the short circuit boundary conditions at the endof the slot antenna. If by using an appropriate boundary condition, themagnetic current density at any arbitrary point |z′|<(λ_(s)/4) along thelength of a modified slot antenna can be maintained the same as the λ/2slot antenna, then it is possible to make a smaller slot antenna. Anysize reduction of interest can be achieved so long as the appropriateBCs are in place at the proper location on the slot. FIG. 8 illustratesthe idea where it is shown that by imposing a finite voltage at bothends of a slot, the desired magnetic current distribution on a shortslot antenna can be established. To create a voltage discontinuity, onecan use a series inductive element at the end of the slot antenna. Itshould be pointed out that terminating the slot antenna with a lumpedinductance or capacitance is not practical since the slot is embedded ina ground plane, which can in fact short-circuit any termination. Tocircumvent this problem, a lumped inductor could be physically realizedby a compact short-circuited slotted spiral. To ensure inductiveloading, the length of the spiral slot must be less than a quarterwavelength Instead of a single inductive element at each end, it ispreferred to use two inductive slotlines opposite of each other (seeFIG. 9A-9C and FIG. 10). Since these two inductors in the slotconfiguration are in series, a shorter slotline provides the requiredinductive load at the end of the slot antenna. Another reason forchoosing this configuration is that the magnetic currents following inopposite directions cancel each other's fields on the planes ofsymmetry, and thereby, minimize the near-field coupling effect of theinductive loads on the desired current distribution along the radiatingslot. It should be noted that the mutual coupling within the spiralslotline reduces the effective inductance and therefore, a longer spirallength compared with a straight section (FIG. 9A-9C) is needed toachieve the desired inductance. To alleviate this adverse effect, anarrower slot width must be chosen for the spiral slotline.

A microstrip transmission line is used to feed this antenna. The choiceof the microstrip feed, as opposed to a coaxial line, is based on theease of fabrication and stability. This feed structure is also moreamenable to tuning by providing the designer with an additionalparameter. Instead of short-circuiting the microstrip line over theslot, an open-ended microstrip line with an appropriate length extendingbeyond the microstrip-slot crossing point (additional parameter) can beused. A Coplanar Waveguide (CPW) can also be used to feed the antennaproviding ease of fabrication, whereas it is more difficult to tune.Usually, a metallic bridge is needed to suppress the odd mode in theCPW. The use of CPW lines also reduces the effective aperture of theslot antenna, especially when a very small antenna is to be matched to a50Ω line. Typically for a low dielectric constant substrate, the centerconductor in the CPW lines at 50Ω is rather wide and the gap between thecenter conductor and the ground planes is relatively narrow. Hence,feeding the slot antenna from the center blocks a considerable portionof the miniaturized slot antenna. There are other methods to feed theslot antenna with CPW lines, including an inductively or capacitivelyfed slot

A procedure according to the present invention provides for designing anovel miniaturized antenna with the topology discussed in the previoussection. To illustrate this procedure, a miniaturized slot antenna at300 MHz is designed. This frequency is the lowest frequency at whichaccurate antenna measurements can be performed in the anechoic chamber,and yet, the miniature antenna is large enough so that standard printedcircuit technology can be used in the fabrication of the antenna. Amicrowave substrate with a dielectric constant of ε_(r)=2.2, a losstangent of tan δ≈10⁻³, and a thickness of 0.787 mm (31 mil) isconsidered for the antenna prototype. TABLE 2 Slotline characteristicsfor two different values of slot width w, and the dielectric constant ofε_(r) = 2.2 and thickness of h = 0.787 (mm) and f = 300 MHz. ω(mm)λ_(s)(mm) Z_(0s)(Ω) 0.5 918 81 3.0 960 107

As the first step, the basic transmission line model is employed todesign the antenna and then, a fill-wave Moment Method analysis is usedfor fine tuning. Table 2 shows the finite ground plane slotlinecharacteristic impedance Z_(0s), and guided wavelength λ_(g), for theabove mentioned substrate and for two slot widths of ω=0.5 mm and ω=3.0mm, all at 300 MHz. As mentioned before, the antenna size can be chosenas a design parameter and in this example, we attempt to design a verysmall antenna with a length of l=55 mm≈0.05λ₀. A slot width of ω=3 mm ischosen for the radiating section of the slot antenna A slot antennawhose radiating slot segment is of a length l, should be terminated by areactance given by $\begin{matrix}{{X_{t} = {Z_{0s}\tan\frac{2\pi}{\lambda_{s}}l^{\prime}}},} & (2)\end{matrix}$in order to maintain the magnetic current distribution of a λs/2resonant slot antenna (see FIG. 2). In equation (2), $\begin{matrix}{{l^{\prime} = {\frac{1}{2}\left( {\frac{\lambda_{s}}{2} - l} \right)}},} & (3)\end{matrix}$and Z_(0s) and λ_(s) are the characteristic impedance and the guidedwavelength of the slotline, respectively. As mentioned before, therequired terminating reactance of X_(t) can be constructed by twosmaller series slotlines. Denoting the length of a terminating slotlineby l″, as shown in FIG. 9A-9C, the relationship between the requiredreactance and l″ is given by $\begin{matrix}{\frac{X_{t}}{2} = {Z_{0s}^{\prime}\tan\frac{2\pi}{\lambda_{0s}^{\prime}}}} & (4)\end{matrix}$where Z′_(0s) and λ′_(0s) are the characteristic impedance and theguided wavelength of the terminating slotline. A narrower slot is usedto construct the terminating slotlines so that a more compactconfiguration can be achieved. As shown in Table 2, the narrowerslotline has a smaller characteristic impedance and guided wavelengthwhich results in a slightly shorter length of the termination (l″).Although l″ is smaller than l′ the actual miniaturization is obtained bywinding the terminating line into a compact spiral as seen in FIG. 10.

According to equation (2) and equation (4), and also the values for theguided wavelengths, l″ is found to be l″=193.7 mm. Referring to FIG. 10,the vertical dimension (along y axis) of the rectangular spiral shouldnot exceed half of the length of the radiating slot segment (l). Thisconstraint on the inductive rectangular spiral is imposed so that theentire antenna structure can fit into a square area of 55 mm×55 mm,which is about 0.05λ₀×0.05λ₀. Since the dielectric constant and thethickness of the substrate chosen for this design are very low(ε_(r)=2.2), the guided wavelength (λ_(g)=96 cm) is not very muchdifferent from that of free space (λ₀=100 cm). Thus, the miniaturizationis mainly achieved by the proper choice of the antenna topology. It isworth mentioning that further size reduction can be obtained once asubstrate with higher permittivity is used.

In the previous section, the transmission line model was employed fordesigning the proposed miniature antenna. Although this model is notvery accurate, it provides the intuition necessary for designing thenovel topology. The transmission line model ignores the coupling betweenthe adjacent slot lines and the microstrip to slot transition. Forcalculation of the input impedance, and exact determination of thelength of different slotline segments, a full-wave simulation tool isrequired. IE3D, a commercially available Moment Method code is used forrequired numerical simulations.

FIG. 10 shows the proposed antenna geometry fed by a two-port 50Ωmicrostrip line. The two-port structure is constructed to study theresonant frequency of the antenna as well as the transition betweenmicrostrip and the slot antenna. The microstrip line is extended wellbeyond the slot transition point so that the port terminals do notcouple to the slot antenna. The radiating slot length is chosen to bel=55 mm, and the length of the rectangular spirals are tuned such thatthe antenna resonates at 300 MHz. The resonance at the desired frequencyis indicated by a deep null in the frequency response of S₂₁. Thesimulated S-parameters of this two-port structure are shown in FIG. 11.This figure indicates that the antenna resonates at around 304 MHz,which is close to the desired frequency of 300 MHz. In fact, theresonant frequency of the radiating structure must be chosen at aslightly higher or lower frequency. The reason is that small slotantennas have a low radiation conductance at the first resonance andtherefore, it should be tuned slightly off-resonance if it is to bematched to a 500 transmission line. FIG. 12 shows an equivalent circuitmodel for the two-port device when the transition between microstrip andslot line is represented by an ideal transformer with a frequencydependent turn ratio (n²), and the slot is modeled by a second ordershunt resonant circuit near its resonance.

The radiation conductance G_(s), which is also referred to as the slotconductance, attains a low value that corresponds to a very high inputimpedance at the resonant frequency. However, this impedance woulddecrease considerably, when the frequency moves off the resonance. The 4MHz offset in the resonant frequency of the antenna is maintained forthis purpose.

Having tuned the resonant frequency of the antenna, coupled to the2-port microstrip feed (FIG. 10), a loss-less impedance matching networkmust be designed. This can be accomplished by providing a properimpedance to terminate the second port of the microstrip feed line. Tofulfill these tasks systematically, we need to extract the equivalentcircuit parameters shown in FIG. 12. It should be pointed out that forthe proposed miniaturized slot antenna, a simplistic model for normalsize slots, which treats the slot antenna as an impedance in series withthe microstrip line is not sufficient. Essentially, the parasiticeffects caused by the coupling between the microstrip feed andrectangular spirals as well as the mutual coupling between the radiatorsection and the rectangular spirals should also be included in theequivalent circuit.

In this section, an equivalent circuit model for the proposed antenna isdeveloped. This model is capable of predicting the slot radiationconductance and the antenna input impedance near resonance. Thisapproach provides a very helpful insight as to how this antenna and itsfeed network operate. As mentioned before, this model is also needed tofind a proper matching network for the antenna. Near resonantfrequencies, the slot antenna can be modeled by a simple second orderRLC circuit. Since the voltage across the slot excites the slot antennaat the feed point, it is appropriate to use the shunt resonant model forthe radiating slot as shown in FIG. 12. The coupling between themicrostrip and the slot is modeled by a series ideal transformer with aturn ratio n.

To model the feeding mechanism right at the cross junction of themicrostrip and slot, it is necessary to de-embed the effect of themicrostrip lines between the terminals and the crossing points. Thereare different de-embedding schemes reported in the literature. Theadvantage of proper de-embedding as opposed to the mere shifting of thereference planes by the corresponding phase factor is to exclude theeffect of radiation and other parasitic effects of the line.

To model the parasitic coupling of the microstrip line and the slot(coupling of radiated field from the microstrip line and slot), twoadditional parasitic parameters, namely, L_(g) and C_(g) are included inthe model The use of shunt parasitic parameter has previously beensuggested to model the effects of fields as perturbed by a wide slot.FIG. 13 shows the de-embedded Y-parameters of the two-portmicrostrip-fed slot antenna where the location of de-embedded ports areshown in FIG. 10. Note that these two ports are now defined at themicrostrip-slot junction According to the lumped element model of FIG.12, the Y-parameters are given by: $\begin{matrix}{Y_{11} = {\frac{- j}{{L_{g}\omega} - \frac{1}{C_{g\quad\omega}}} + {\frac{1}{n^{2}}\left\lbrack {G_{s} + {j\left( {{C_{s}\omega} - \frac{1}{L_{s}\omega}} \right)}} \right\rbrack}}} & (5) \\{Y_{21} = {- {\frac{1}{n^{2}}\left\lbrack {G_{s} + {j\left( {{C_{s}\omega} - \frac{1}{L_{s}\omega}} \right)}} \right\rbrack}}} & (6)\end{matrix}$Using reciprocity and noting the symmetry of the equivalent circuit, itcan easily be shown that Y₁₁=Y₂₂ and Y₂₁=Y₁₂.

In order to extract the equivalent circuit parameters, a GeneticAlgorithm (GA) optimization code has been developed and implemented. Thesum of the squares of relative error for real and imaginary parts ofY-parameters over 40 frequency points around the resonance is used asthe objective (fitness) function of the optimization problem. Theprogram can be run with different random number seeds to ensure the bestresult over the entire domain of the parameters space. Also, theparameters were constrained only to physical values in the region ofinterest. The parameters of the GA optimizer are shown in Table 3. Table4 shows the extracted equivalent circuit parameters after fiftythousands iterations. TABLE 3 The parameters of the Genetic Algorithmoptimizer. Population Size 300 Number of Iteration 50,000 ChromosomeLength 128 P_(Crossover) 0.55 P_(Mutation) 0.005

The S-parameters of the equivalent circuit as well as the S-parametersextracted from the full-wave analysis are shown in FIGS. 14A, 14B, 14C,and 14D. Excellent agreement is observed between the full-wave resultsand those of the equivalent circuit. TABLE 4 The equivalent circuitparameters of the microstrip fed slot antenna. Turn Ratio (n) 0.948007R_(s) (Ω) 33979 L_(s) (μH) 0.0207 C_(s) (pF) 13.1744 L_(g) (μH) 0.49997C_(g) (pF) 0.125

Having found the equivalent circuit parameters, the antenna's matchingnetwork can readily be designed. For matching networks, especially whenthe efficiency is the main concern, loss-less terminations are usuallydesired. Therefore, a purely reactive admittance is sought to terminatethe feed line, which in fact is the load for the second port of thetwo-port equivalent circuit model. The explicit expression for atermination admittance (Y_(t)) to be placed at the second terminal ofthe two-port model in order to match the impedance of the antenna isgiven by: $\begin{matrix}{Y_{t} = {{- Y_{11}} + \frac{Y_{12}^{2}}{Y_{11} - Y_{0}}}} & (7)\end{matrix}$

FIG. 15 shows the spectral behavior of Y_(t) for a standard 50Ω line(Y₀=0.02

). Interesting to note are the two distinct frequency points at whichthe real part of Y_(t) vanishes. This implies that this antenna can bematched at these two frequency points, namely, 300 MHz and 309 MHz. Asmentioned earlier, a small slot antenna has a very low radiationconductance.

The value of this low conductance, as can be found in Table 4 suggests avery high input impedance of the order of 30KΩ at resonance, consideringthe transformer turn ratio. Thus, in order to match the antenna to alower impedance transmission line, the matching should be done at afrequency slightly off the resonance. At an off-resonance frequency, theinput impedance does not remain a pure real quantity, however, theimaginary part can easily be compensated for by an additional reactivecomponent created by an open-ended microstrip. At each resonance, thereare two possibilities. One possibility is to match the antenna slightlybelow the slot resonance, that is 304 MHz (FIG. 11), and terminate thesecond port capacitively. The second possibility is to tune the antennaslightly above the slot resonance and terminate the second portinductively. TABLE 5 The physical length of the 50Ω microstrip lineneeded for realizing the termination susceptance, where the dielectricmaterial properties are as specified in Table 2. f (MHZ) 300 309Y_(t)(s) j5.4 × 10⁻⁴ −j1.14 × 10⁻³ λ_(g)(mm) 725.57 704.52 Z₀(Ω) 50 50Line extension (mm) 3.1514 345.80

Based on what is shown in Table 5, a very short open-ended-microstripline extension is required at the second port, in contrast with aquarter wavelength extension for an ordinary half wavelength slotantenna This short extension introduces a small capacitance, whichcompensates the additional inductance introduced as a result ofoperating below resonance. After tuning the antenna, the original slotresonant frequency at 304 MHz, shifts down to the desired frequency of300 MHz, as shown in FIG. 15 and Table 5.

EXAMPLE III

In this section, simulation results for the antenna according to thepresent invention are illustrated. FIG. 17 shows the antenna geometrymatched to a 50Ω line. As seen in FIG. 17 and suggested by Table 5, thefeed line has been extended a short distance beyond the slot line. Thewidth of the microstrip where it crosses the slot is reduced so that itmay block a smaller portion of the radiating slot. It is worthmentioning that the effect of the feed line width on its coupling to theslot was investigated, and it was found that as long as the line widthis much smaller than the radiating slot length, the equivalent circuitparameters do not change considerably.

As mentioned, the antenna has been simulated using a commercial software(IE3D). Using this software, the return loss (S₁₁) of the antenna iscalculated and shown in FIG. 16. In order to experimentally validate thedesign procedure, equivalent circuit model and simulation results, theantenna was fabricated on a 0.787 mm-thick substrate with ε_(r)=2.2 andtan δ=0.001.

FIG. 18 shows a photograph of the fabricated antenna. The return loss(S₁₁) of the antenna was measured using a calibrated vector networkanalyzer and the result is shown in FIG. 16. The measured results show aslight shift in the resonant frequency of the antenna (≈1%) from what ispredicted by the numerical code. The errors associated with thenumerical code could contribute to this frequency shift. This deviationcan also be attributed to the finite size of the ground plane,0.21λ₀×0.18λ₀ for this prototype, knowing that an infinite ground planeis assumed in the numerical simulation.

The far field radiation patterns of the antenna were measured in theanechoic chamber of The University of Michigan. The gain of the antennawas measured at the bore-sight direction under polarization-matchedcondition using a standard antenna whose gain is known as a function offrequency. The gain of −3 dB, (relative to an isotropic radiator) wasmeasured. Having perfectly matched the impedance of the antenna, thesimulated efficiency of this antenna is found to be η=67% (−1.75 dB),which can exclusively be attributed to Ohmic and dielectric losses. Thesimulated radiation efficiency is the ratio of the total radiated powerto the input power of the antenna. The directivity of this antenna (withinfinite ground plane) was computed to be D=2.0 dB. This value ofdirectivity is very close to that of a dipole antenna. Based on thedefinition of the antenna gain, under the impedance matched condition,one might expect to measure the maximum gain ofG=η·D=−1.75 dB+2.5 dB=0.75 dB  (8)

for this antenna. There is still a considerable difference between themeasured and simulated gains (about 3.75 dB), which stems from two majorfactors. First, in the simulation, an infinite ground plane is assumed,whereas the actual ground plane size for the measured antenna isapproximately 0.2λ₀×0.24λ₀. As the ground plane size decreases, thelevel of electric current around the edges increases considerably. Thisincrease in the level of the electric current results in an additionalOhmic loss compared to the infinite ground plane. Another reason is thatas the ground plane size decreases, the directivity of the slot antennais reduced. Basically, as the ground plane becomes smaller, the null inthe pattern diminishes and the pattern approaches that of an isotropicradiator. The reduction in the directivity of the slot antenna with afinite ground plane can also be attributed to the radiation from theedges and surface wave diffraction. To further study the effect of thesize of the ground plane, the same antenna with a slightly larger groundplane (0.58λ₀×0.43λ₀) was fabricated and measured. Table 6 shows thecomparison between the radiation characteristics of these two antennasand simulated results. As explained, when the size of the antenna groundplane increases, the gain of the antenna increases from −3.0 dB, to 0.6dB_(i), which is almost equal to the gain of a half wavelength dipoleand very close to the simulated value for the antenna gain. TABLE 6Antenna characteristics as a function of two different size groundplanes compared with the simulated results for the same antenna on aninfinite ground plane. Ground-Plane Resonant Return Antenna sizefrequency Loss Gain [cm] [MHZ] [dB] [dB_(i)] 21 × 18 298.1 −27 −3.0 58 ×43 298.8 −30 0.6 simulation(∞) 300 <−30 0.75

Finally, the radiation patterns of the proposed antenna in the principalE- and H-plane were measured and compared with the theoretical ones. ForH-plane pattern, E_(φ)(θ) in the φ=90° plane was measured, and forB-plane pattern, E_(θ)(θ) was measured in the φ=0°. The simulatedradiation patterns of this antenna are shown in FIG. 19. It is seen thatthe simulated radiation patterns of the proposed antenna with aninfinite ground plane is almost the same as that of an infinitesimalslot dipole. FIGS. 20A and 20B show the normalized co- andcross-polarized radiation patterns of the H- and E-plane, respectively,for two different ground planes. As expected, the null in the H-planeradiation pattern is filled considerably owing to the finite groundplane size. The ground plane enforces the tangential E-field, E_(φ)(θ),to vanish along the radiating slot at θ=90°, which in fact creates thenull in the H-plane pattern. On the other hand, a deep null in themeasured E-plane pattern is observed, whereas in simulation this cut ofthe pattern is constant except at the dielectric-air interface where thenormal E-field is discontinuous. This null in the E-plane is the resultof the cancellation of fields, which are radiated by the two opposingmagnetic currents. The equivalent magnetic currents, flowing in theupper and lower side of the ground plane, are in opposite directions andconsequently, their radiation in the point of symmetry at the E-planecancel each other. However, in the case of an infinite ground plane, theupper and lower half-spaces are isolated and therefore, the E-planeradiation pattern remains constant.

Moreover, an increase in the measured cross-polarized component isobserved as compared with the simulation results. Although it may seemthat there is a considerable cross polarization radiation due to thepresence of spiral slots at the terminations, there is no such componentin the principal planes as well as the φ=±45° planes since the geometryis symmetric with respect to those planes. The cross polarizationappearing in these measurements is mainly caused by radiation from theedges as well as the feed cable.

The contribution of the anechoic chamber, giving rise to thecross-polarized component at the low frequency of 300 MHz is also afactor. The radiated field of the antenna is always capable of inducingcurrents on the feeding cable, especially when the ground plane size isvery small compared to the wavelength. Then, the induced currentsre-radiate and give rise to the cross polarization. Nevertheless, bothof the above mentioned sources for the cross-polarization can beeliminated by increasing the ground plane size.

A procedure for designing a new class of miniaturized slot antennasaccording to the present invention has been disclosed. In this designthe area occupied by the antenna can be chosen arbitrarily small,depending on the applications at hand and the trade-off between theantenna size and the required bandwidth. As an example, an antenna withthe dimensions 0.05λ₀×0.05λ₀ was designed at 300 MHz and perfectlymatched to a 50Ω transmission line. In this prototype, a substrate witha low dielectric constant of ε_(r)=2.2 was used to ensure that thedielectric material would not contribute to the antenna miniaturization.An equivalent circuit for the antenna was developed, which provided theguidelines necessary for designing a compact loss-less matching networkfor the antenna. To validate the design procedure, a prototype antennawas fabricated and measured at 300 MHz. A perfect match for this verysmall antenna was demonstrated with a moderate gain of −3.0 dB_(i) whenthe antenna is fabricated on a very small ground plane with theapproximate dimensions of 0.2λ₀×0.2λ₀. The gain of this antenna canincrease to that of a half-wave dipole when a slightly larger groundplane of about 0.5λ₀×0.5λ₀ is used. The fractional bandwidth for thisantenna was measured to be 0.4%.

A new miniaturized antenna structure according to the present inventionis disclosed with a larger radiation conductance (physical aperture),bandwidth, and efficiency, while maintaining the size of the antenna.Conversely, maintaining the bandwidth and efficiency, this structure canbe further miniaturized (0.03λ₀×0.03λ₀). The structure according to thepresent invention is based on a folded slot design whose geometry isshown in FIG. 21. The physical aperture of the miniaturized folded slotis twice as large as that of the miniaturized slot illustrated in FIG.1A, and therefore, should demonstrate a radiation conductance four timesas high as the design of FIG. 1A In order to specify the resonantfrequency and radiation resistance of the folded-slot structure, theantenna was center-fed with a CPW line and was simulated using acommercially available Moment Method code. FIGS. 22A and 22B show acomparison between the input impedance of the folded design, and thesingle slot of FIG. 1A, where it can be seen that the impedance of thefolded slot antenna is reduced by a factor of four, relative to that ofthe narrow slot design. Therefore, a much smaller reactance is needed tomatch the impedance to a 50Ω line. In fact, the closer the impedance ofthe antenna is to 50Ω, the easier it is to match, and the wider thefrequency band over which impedance matching can be expected. There aretwo choices to achieve impedance match: one is to tune it belowresonance where the slot is inductive and then, compensate thatinductance with a capacitive coupling at the feed, and the other is toinductively feed the slot slightly above its resonance. Since it isdesirable to minimize the antenna size, a capacitively fed slot antennais preferred. FIG. 23 shows the miniaturized folded slot antenna matchedto a 50Ω CPW line. The proper value of the capacitance to be inserted inthe feed is determined from a second order resonant equivalent circuitmodel. These model parameters can be extracted using a full wavesimulation of the antenna structure. The folded slot has a resonance at337.9 MHZ with a radiation resistance of about 5KΩ, as shown in FIG.22A. After insertion of a tuning capacitance, the antenna is matched to50Ω at a slightly lower frequency of 336.1 MHZ. (See FIG. 24).

EXAMPLE IV

The miniaturized folded slot shown in FIG. 23., was fabricated on a0.762 mm thick RT Duroid 5880 and its impedance and radiationcharacteristics were investigated in order to validate simulationresults. The simulated and measured return losses for the folded antennaare shown in FIG. 24, where it is shown that a perfect impedance matchis achieved. There is a % 1 shift in the resonant frequency of thematched antenna compared to the results obtained from the simulation.This discrepancy can be attributed to the finite size of theground-plane, numerical error, and the underestimation of the dielectricloss tangent of the substrate. FIG. 16 shows the same data sets for aminiaturized single slot antenna, having approximately the same size.Comparison of FIGS. 24 and 16, clearly indicates an increase in the −10dB return-loss bandwidth of the antenna. Table 7, shows a comparisonbetween both simulated and measured bandwidths of these two antennas.TABLE 7 Comparison between miniaturized slot and miniaturized foldedslot antennas. Antenna BW (%) Gain (dBi) Directivity Type Size Sim measSim meas (dB) Miniature 0.05λ₀ × 0.05λ₀ 0.058 0.34 1.0 −3.0 1.9 slotFolded 0.067λ₀ × 0.067λ₀ 0.12 0.93 1.0 −2.7 1.8 slotIt should be pointed out that there is a considerable difference betweenthe simulated and measured bandwidths. This variation stems from thefact that some losses are not accounted for in the simulation, includingthe increased conduction loss generated by the edge currents around theedges of the ground plane and also the radiation from edges of thesubstrate. The gain of this antenna was determined with reference to astandard half wavelength dipole antenna. A gain of −2.7 dB over the gainof a standard λ/2 dipole was measured. The gain of a standard dipole isassumed to be 0 dBi. This measured value is lower than the simulatedresults, which again can be attributed to the finite size of the groundplane. As the size of ground plane is increased, the measured resultsconverge to that of the simulation. Finally, the E-plane and H-planeradiation patterns of the antenna were measured in the anechoic chamberand the results are shown in FIGS. 25A and 25B. FIG. 26 depicts thesimulated radiation pattern of the total field and shows that thisstructure has a pattern very similar to that of a small dipole. Thecross polarization components are negligible in the principal planes.The observed cross-polarized radiation is believed to emanate fromfeeding cables rather than from the antenna itself

A miniaturized folded slot antenna according to the present inventionpresents an improved configuration for miniaturized slot antennas, whichdemonstrates wider bandwidth and higher radiation efficiency. By fixingthe size of the configuration to 0.06λ₀×0.06λ₀, which is almost the sameas dimensions of the miniaturized slot antenna, the bandwidth of theantenna was increased by 100% with a slight increase in the gain of theantenna.

While the invention has been described in connection with what ispresently considered to be the most practical and preferred embodiment,it is to be understood that the invention is not to be limited to thedisclosed embodiments but, on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims, which scope is to be accorded the broadestinterpretation so as to encompass all such modifications and equivalentstructures as is permitted under the law.

1. A miniaturized antenna for sending and receiving a signal having awavelength comprising: a substrate; and a slot dipole line formed on thesubstrate with an electrical length less than a quarter wavelength and ashort circuit at one end and an open circuit at an opposite end.
 2. Theantenna of claim 1 further comprising: the open circuit of the slotdipole line including two non-radiating spiral slots formed assymmetrical mirror images of one another and short circuited at one end.3. The antenna of claim 2 further comprising: the two non-radiatingspiral slots having less than a quarter wavelength.
 4. The antenna ofclaim 1 further comprising: a bent radiating section of the slot line.5. The antenna of claim 4 further comprising: the bent radiating sectionhaving at least two portions extending angularly with respect to oneanother so that no portion carries a magnetic current opposing amagnetic current of any other portion.
 6. The antenna of claim 5 furthercomprising: a T-shaped end formed on the radiating section.
 7. Theantenna of claim 1 further comprising: an open ended microstrip linefeeding the slot dipole line of the antenna at a crossing point andextending less than a quarter wavelength.
 8. The antenna of claim 1further comprising: the slot dipole line having a radiating section withthree line portions bent with respect to one another, where one lineportion has a width less than a width of other line portions.
 9. Theantenna of claim 8 further comprising: relative lengths of each lineportion selected to minimize an area occupied by the slot line.
 10. Theantenna of claim 1 further comprising: two inductive short-circuitedspiral slot lines terminating each end of a straight line section of theslot dipole line, each spiral slot line having a length less than aquarter wavelength while being greater than a straight section of theslot dipole line and having a narrower slot width than the straight linesection, the two inductive short-circuited spiral slot lines formed asmirror images of each other one each end of the straight line section ofthe slot dipole line.
 11. The antenna of claim 10 further comprising: adimension of the substrate selected for sizing the antenna between0.01λ₀ and less than 0.50λ₀.
 12. The antenna of claim 10 furthercomprising: a dimension of the substrate selected for sizing the antennabetween 0.05λ₀ and 0.25λ₀.
 13. The antenna of claim 10 furthercomprising: a very high impedance on an order of 5,000 to 15,000. 14.The antenna of claim 10 further comprising: a very high impedance on anorder of 10,000.
 15. The antenna of claim 10 further comprising: eachspiral slot line coiled in a pattern with a maximum dimension less thanone-half of a length of a radiating slot section.
 16. The antenna ofclaim 10 further comprising: the slot dipole line including a foldedslot line.
 17. The antenna of claim 16 further comprising: a coplanarwaveguide line center-feeding the folded slot line.
 18. The antenna ofclaim 10 further comprising: an open ended microstrip line feeding theslot dipole line at a crossing point.
 19. The antenna of claim 18further comprising: the microstrip line extending beyond the slot dipoleline defining a second port with small capacitance.
 20. The antenna ofclaim 19 further comprising: a width of the microstrip line reduced atthe crossing point of the slot dipole line.
 21. The antenna of claim 1further comprising: wherein the antenna is operably coupled with respectto a mobile apparatus selected from a group including an electronicchip, a laptop computer, a body of a motor vehicle, a mirror of a motorvehicle, an aircraft body component, and a missile body component. 22.The antenna of claim 1 further comprising: the substrate being planarand low profile with a relatively thin thickness and having dimensionsof length and width less than one-half the wavelength to be sent andreceived.
 23. The antenna of claim 1 further comprising: the antennabeing monolithic, integrated, and resonant.
 24. A miniaturized antennafor sending and receiving a signal having a wavelength comprising: asubstrate; a slot dipole line formed on the substrate with an electricallength less than a quarter wavelength and a short circuit at one end andan open circuit at an opposite end, the open circuit of the slot dipoleline including two non-radiating spiral slots formed as symmetricalmirror images of one another and short circuited at one end, the slotdipole line having a radiating section with three line portions bentwith respect to one another, where one line portion has a width lessthan a width of other line portions, the line portions extendingangularly with respect to one another so that no line portion carries amagnetic current opposing a magnetic current of any other line portion;and an open ended microstrip line feeding the slot dipole line at acrossing point and extending less than a quarter wavelength.
 25. Amethod for designing a miniaturized slot antenna comprising the stepsof: arbitrarily selecting dimensions of the antenna; feeding the antennawith one of a microstrip line and a CPW line; finding an antennaresonant frequency by locating a null in insertion loss; and determininga loss-less termination impedance end of the one of the microstrip lineand CPW line to achieve a perfect match.